The invention relates generally to equalizer circuits and more particularly to an equalizer providing double differentiation without introducing phase shift for all values of input frequency and equalization boost.
Equalizers for use in audio and video systems have been known variously as crispeners, aperture correctors, contour enhancers, shapers, and the like. Typically such circuits are employed to restore high frequency components to waveforms that have suffered loss or degradation of their high frequency information due to processing by bandwidth limited devices. For example, communications links and the record/playback process of magnetic tape and disc equipment often removes or suppresses the high frequency portions of the original signal. In terms of a reproduced television picture, loss of edge definition is the most apparent effect. Equalizers have therefore operated to modify the system degraded waveform in some manner in an attempt to bring it closer to its original form.
One well-known approach in equalizers restoring lost high frequency information is to combine with the main signal a supplemental signal having an amplitude related to the square of the signal frequency. For an input U.sub.i, the output is U.sub.o = U.sub.i (1 .+-. k.omega..sup.2). Thus, for higher frequencies the output signal is boosted.
Such a correction is theoretically achievable by double differentiation. However, true double differentiation has heretofore been achieved only within narrow limits of input signal frequency. True differentiation is of the form EQU A(.omega.) = .omega..tau.,
whereas the conventional differentiator circuit provides a transfer function of the form ##EQU1## This function approximates true differentiation only for small values of .omega..tau. as seen in FIG. 1 which shows plots of A(.omega.) versus .omega..tau. for true and conventional differentiation.
Double differentiation achieved by conventional differentiation circuits results in the function shown in FIG. 1. Beyond small values of .omega..tau., this function departs radically from the true double differentiation curve (.omega..tau.).sup.2.
Such conventional double differentiation techniques introduce significant phase shift, except at small values of .omega..tau.. Many signal processing applications are extremely sensitive to phase shift, making such prior art techniques unacceptable.